Optimal. Leaf size=22 \[ \frac {\left (2+4 x^2\right )^2}{\left (\frac {x^3}{400}+\log (x)\right )^2} \]
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Rubi [F] time = 1.20, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-512000000-2048000000 x^2-3840000 x^3-2048000000 x^4-10240000 x^5-5120000 x^7+\left (2048000000 x^2+4096000000 x^4\right ) \log (x)}{x^{10}+1200 x^7 \log (x)+480000 x^4 \log ^2(x)+64000000 x \log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1280000 \left (1+2 x^2\right ) \left (-400-800 x^2-3 x^3-2 x^5+1600 x^2 \log (x)\right )}{x \left (x^3+400 \log (x)\right )^3} \, dx\\ &=1280000 \int \frac {\left (1+2 x^2\right ) \left (-400-800 x^2-3 x^3-2 x^5+1600 x^2 \log (x)\right )}{x \left (x^3+400 \log (x)\right )^3} \, dx\\ &=1280000 \int \left (-\frac {\left (1+2 x^2\right )^2 \left (400+3 x^3\right )}{x \left (x^3+400 \log (x)\right )^3}+\frac {4 x \left (1+2 x^2\right )}{\left (x^3+400 \log (x)\right )^2}\right ) \, dx\\ &=-\left (1280000 \int \frac {\left (1+2 x^2\right )^2 \left (400+3 x^3\right )}{x \left (x^3+400 \log (x)\right )^3} \, dx\right )+5120000 \int \frac {x \left (1+2 x^2\right )}{\left (x^3+400 \log (x)\right )^2} \, dx\\ &=-\left (1280000 \int \left (\frac {400}{x \left (x^3+400 \log (x)\right )^3}+\frac {1600 x}{\left (x^3+400 \log (x)\right )^3}+\frac {3 x^2}{\left (x^3+400 \log (x)\right )^3}+\frac {1600 x^3}{\left (x^3+400 \log (x)\right )^3}+\frac {12 x^4}{\left (x^3+400 \log (x)\right )^3}+\frac {12 x^6}{\left (x^3+400 \log (x)\right )^3}\right ) \, dx\right )+5120000 \int \left (\frac {x}{\left (x^3+400 \log (x)\right )^2}+\frac {2 x^3}{\left (x^3+400 \log (x)\right )^2}\right ) \, dx\\ &=-\left (3840000 \int \frac {x^2}{\left (x^3+400 \log (x)\right )^3} \, dx\right )+5120000 \int \frac {x}{\left (x^3+400 \log (x)\right )^2} \, dx+10240000 \int \frac {x^3}{\left (x^3+400 \log (x)\right )^2} \, dx-15360000 \int \frac {x^4}{\left (x^3+400 \log (x)\right )^3} \, dx-15360000 \int \frac {x^6}{\left (x^3+400 \log (x)\right )^3} \, dx-512000000 \int \frac {1}{x \left (x^3+400 \log (x)\right )^3} \, dx-2048000000 \int \frac {x}{\left (x^3+400 \log (x)\right )^3} \, dx-2048000000 \int \frac {x^3}{\left (x^3+400 \log (x)\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.34, size = 21, normalized size = 0.95 \begin {gather*} \frac {640000 \left (1+2 x^2\right )^2}{\left (x^3+400 \log (x)\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 33, normalized size = 1.50 \begin {gather*} \frac {640000 \, {\left (4 \, x^{4} + 4 \, x^{2} + 1\right )}}{x^{6} + 800 \, x^{3} \log \relax (x) + 160000 \, \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 71, normalized size = 3.23 \begin {gather*} \frac {640000 \, {\left (12 \, x^{7} + 12 \, x^{5} + 1600 \, x^{4} + 3 \, x^{3} + 1600 \, x^{2} + 400\right )}}{3 \, x^{9} + 2400 \, x^{6} \log \relax (x) + 400 \, x^{6} + 480000 \, x^{3} \log \relax (x)^{2} + 320000 \, x^{3} \log \relax (x) + 64000000 \, \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 25, normalized size = 1.14
method | result | size |
risch | \(\frac {2560000 x^{4}+2560000 x^{2}+640000}{\left (x^{3}+400 \ln \relax (x )\right )^{2}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 33, normalized size = 1.50 \begin {gather*} \frac {640000 \, {\left (4 \, x^{4} + 4 \, x^{2} + 1\right )}}{x^{6} + 800 \, x^{3} \log \relax (x) + 160000 \, \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.40, size = 21, normalized size = 0.95 \begin {gather*} \frac {640000\,{\left (2\,x^2+1\right )}^2}{{\left (400\,\ln \relax (x)+x^3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 29, normalized size = 1.32 \begin {gather*} \frac {2560000 x^{4} + 2560000 x^{2} + 640000}{x^{6} + 800 x^{3} \log {\relax (x )} + 160000 \log {\relax (x )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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